Elliptic Problems with Singular Potential and Double-Power Nonlinearity

We prove the existence of positive symmetric solutions to the semilinear elliptic problem in both the radial case N = k ≥ 3 and the cylindrical case N ≥ k + 3 ≥ 6. The potential V is measurable, positive and it is only required to satisfy a mild integrability condition. The nonlinearity is continuous and has a doublepower behavior, super-critical near the origin and sub-critical at infinity. If f is odd, we show that the radial problem has infinitely many solutions. In proving these results we exploit the compactness of suitable restrictions of the embedding Supported by MIUR, project “Variational Methods and Nonlinear Differential Equations”.